A generalized criterion for parametric sensitivity: Application to thermal explosion theory

A new criterion for parametric sensitivity or thermal runaway is proposed in the context of thermal explosions, which can also be readily utilized for chemical reactors. Criticality is defined as the situation where the normalized objective sensitivity, of the temperature maximum to any of the physicochemical parameters of the model, is a maximum. In fact it is found that, in all cases of practical interest, the region of sensitivity obtained with respect to any of the independent model input parameters is the same. Thus, this criterion predicts a parametrically sensitive or runaway region, which may be called “generalized” since the maximum temperature becomes simultaneously sensitive to small changes of any of the model inputs. The proposed criterion exhibits a highly intrinsic nature and it is firmly based on the rigorous concept of normalized sensitivity. This, together with its flexibility, allows direct extension of the criterion to more general problems, both in thermal explosion and in chemical reaction engineering fields. This is especially so for cases where it may be convenient or desirable to consider the sensitivity of outputs of the model other than the maximum temperature, and/or cases where a temperature profile does not even exist, e.g. in a CSTR. None of these situations can be handled with sensitivity criteria previously available in the literature, since they are all based on the topology of some type of a temperature profile.